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Harvey P. Dale, <a href="/A258823/b258823.txt">Table of n, a(n) for n = 1..1000</a>

kQ[n_]:=Module[{tr=Rest[NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&]], len}, len = Length[ tr]; Count[Thread[{tr, Range[len]}], _?(#[[1]] == #[[2]]&)]>0]; Select[Range[300], kQ] (* Harvey P. Dale, Jan 13 2017 *)

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proposed

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allocated Numbers n such that k iterations of n under the '3x+1' map yield k for Derek Orrsome k.

2, 7, 8, 10, 18, 19, 24, 26, 41, 43, 44, 45, 46, 48, 52, 53, 64, 65, 66, 67, 72, 74, 76, 77, 97, 98, 99, 100, 101, 102, 112, 116, 117, 120, 122, 144, 148, 149, 153, 156, 157, 158, 160, 172, 173, 174, 175, 209, 210, 211, 246, 247, 248, 249, 250, 252, 253, 254, 255, 260, 261, 262, 264, 266, 268, 269, 272

1,1

Numbers n such that A258822(n) > 0.

For n = 6, the '3x+1' map is as follows: 6 -> 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1. For any possible k, after the k-th iteration, the result does not equal k. Thus 6 is not a member of this sequence.

For n = 7, the '3x+1' map is as follows: 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1. After 10 iterations, we arrive at 10. So, 7 is a member of this sequence.

(PARI) Tvect(n)=v=[n]; while(n!=1, if(n%2, k=3*n+1; v=concat(v, k); n=k); if(!(n%2), k=n/2; v=concat(v, k); n=k)); v

n=1; while(n<10^3, d=Tvect(n); c=0; for(i=1, #d, if(d[i]==i-1, print1(n, ", "); break)); n++)

Cf. A258822, A006370, A070165.

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nonn

Derek Orr, Jun 11 2015

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allocated for Derek Orr

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